The primary components of successful engineering projects are time, cost, and quality. The use of the ring footing ensures the presence of these elements. This investigation aims to find the optimum number of geogrid reinforcement layers under ring footing subjected to inclined loading. For this purpose, experimental models were used. The parameters were studied to find the optimum geogrid layers number, including the optimum geogrid layers spacing and the optimum geogrid layers number. The optimum geogrid layers spacing value is 0.5B. And as the load inclination angle increased, the tilting and the tilting improvement percent for the load inclination angles (5°,10°,15°) are (40%,28%, and 5%) respectively. The reduction percent of the lateral displacement for the spacing ratio (0.5B,0.75B,1B,1.25B) are (16%,10%,8%,7%), respectively. The optimum geogrid layers number is found to be 4. As the load inclination angle increased, the tilting and the tilting improvement percent for the load inclination angles (5°,10°,15°) are (45%,33%, and 8%), respectively. The reduction percent of the lateral displacement for the reinforcement layers number (1,2,3,4) are (12%,16%,18%,20%), respectively
Let R be a commutative ring with unity and an R-submodule N is called semimaximal if and only if
the sufficient conditions of F-submodules to be semimaximal .Also the concepts of (simple , semisimple) F- submodules and quotient F- modules are introduced and given some properties .